Literacy in Mathematics

Understanding the Importance of Reading and Writing in Mathematics Lessons Patricia J. Guajardo EDUC4345G Our Lady of the Lake University November 29, 2011 Abstract Understanding literacy in Math means more than just knowing the basic skills of addition, subtraction, multiplication and division. Mathematics is made of letters, numbers, symbols, and a vocabulary that form a language all its own. It is important for teachers to understand the complexities of Math and how to share strategies of learning for student success.

Some research suggests a lack of prior knowledge and basic skills and others suggest a breakdown in the system. Regardless, student success is dependent upon an understanding of the literacy of Math and the ability to teach all students to be successful. Introduction Math is all around us. We learn Math in school and use it in our daily lives; often not realizing we are performing Math functions. Literacy in Math is essential; however, there are many factors that are preventing students from succeeding in the Math. Research shows that reading and writing in Math are critical to success in Math.

If students are fluent in reading, one would assume fluency in Math as well. However, this is not the case. According to the National Assessment of Educational Progress (NAEP), 32% of eighth graders have attained a “proficient” level on reading scores leveling many children who are not as fluent in reading materials, making inferences, and thinking critically as teachers expect or would like (Richardson, Morgan, and Fleener, 2006).

If only 32% of students are proficient in reading, what does that do to Math scores? Math is a language unto itself and is often a challenge to many students, but if you cannot ead well what does this to do achievement scores in Math. My research has indicated that literacy in Math is the key to success in Math. Therefore the answer should be simple: teach students to understand the language of Math. However, research indicates that many students lack prior knowledge, basic facts, ability to read, mathematical thinking/interpretation skills, and confidence (Amen, 2006). Lui (2006) stated No Child Left Behind produced a policy environment with no one left responsible for the “savage inequalities” between affluent schools and those in poor communities of color.

Regardless of who may be to blame for the breakdown in the education system the only way out of this is to focus on educating our students. My goal is to teach Math to secondary students. To achieve this goal, I need to understand literacy in Math, its importance, and how to help students become successful. This paper will examine literacy in Math and the importance of reading and writing in the Math class to fully comprehend the functions of Math. Literacy in Math Kilpatrick (2001) identifies five strands of mathematical proficiency.

They are conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition. Conceptual understanding refers to a student’s comprehension of mathematical concepts, operations and relations. Procedural fluency refers to a student’s skill in carrying out mathematical procedures appropriately. Strategic competence is the student’s ability to formulate, represent, and solve mathematical problems. Adaptive reasoning refers to the capacity for logical thought and for the reflection on, explanation of, and justification of mathematical arguments.

Productive disposition is the student’s habitual inclination to see mathematics as a sensible, useful, and worthwhile subject to be learned, coupled with a belief in the value of diligent work and in one’s own efficacy as a doer of mathematics. Based on Kilpatrick’s definition of mathematical proficiency, it is clear that Math is a very complex subject and requires much understanding. As a result, literacy in Math is a necessity because Math is a language all its own. It is far more than just words on a page.

It is numbers, letters, symbols, and most importantly, it is vocabulary. Students must understand symbols that represent concepts, syntax of a mathematical sentence, and the vocabulary of mathematics (Kester Phillips, Bardsley, Back & Gibbs-Brown, 2000). Fuentes (1998) stated each word and symbol read in mathematics text must be read and understood with precision. It is a misconception that Math is nothing more than addition, subtraction, multiplication, and division. Vocabulary is very important to understanding Math and an important part of the learning process.

To be successful, students need to be fluent readers, but they must also read the text in a specific manner. Dr. Kevin Lee (2010), a professor at Purdue University, suggested the following tips for reading Mathematics: * Focus on concepts not exercises * Read the text more than once * When reading through for the first time, scan for big ideas * The second time through, fill in details * Read with paper, pen and calculator * Read the narrative * Study the examples * Read the pictures * Learn the vocabulary and the language * Use the index and the appendices.

Know what every word means * Make a note of things you don’t understand, ask for help afterwards Following these steps may be timely, but they are necessary if one truly wants to understand the lesson. As students read, they should make notes to the side and go back to those notes to define any words that they don’t know. Students should also study all examples and pictures. Examples and pictures are included for a reason. They are used to help convey the message of the text and explain how to perform functions and calculations. The Breakdown In the introduction I mentioned the breakdown in literacy in Math.

The two main reasons I mentioned was that the No Child Left Behind legislature left gaps in responsibility for the differences in affluent schools versus poor communities of color and the lack of prior knowledge and basic facts. Amen (2006) concluded that students have lower achievement in Math because they lack prior knowledge, basic facts, ability to read, mathematical thinking/interpretation skills and confidence. In Amen’s experience in her own classroom, children of poverty come with fewer opportunities than the children of the middle class.

In addition to battling the issues that many of them face at home each day (hunger, neglect, physical abuse, substance abuse, and non-permanent homes) I also have to deal with the fact that they also come to school less academically prepared than their middle class counterparts. Amen was not suggesting that these students are not able to learn, but that they lack many of the basic skills and knowledge more readily available to students from middle or upper class areas. In his study of the social injustices of reading and writing in Math, Yang (2009) looked at the textbooks and available extensions (audio, video, etc).

Yang looked at the social injustices from both the teacher and student perspectives. Yang’s findings showed that students needed to rely on outside mentoring and tutoring to understand the textbooks. The textbooks were highly technical and students from the poorer communities had many challenges. Now that it is clear there is a breakdown in Math literacy, the question is what to do to rebuild and teach students to become literate. The solution is to determine where students are lacking and focus on building on the skills required and the confidence needed to be successful.

The reading tips mentioned earlier are important, but they are not enough. The ability to read and understand Math and its vocabulary is essential but if students are lacking in the prior knowledge and basic skills of Math, we must address the importance of how to teach those concepts to students. To teach literacy in Math, teachers need to address the two key factors essential to achievement for students: writing in Math and vocabulary development. Importance of Writing in Math According to Schwarz (1999) writing and vocabulary development is necessary in all curricular areas, especially Math.

Writing in Math does not necessarily mean writing an equation. Writing equations is definitely part of fluency and comprehension of math, but when thinking in terms of literacy writing in Math means that students can put into their own words what each lesson means to them. Writing can play a vital role in developing literacy and understanding. According to Blessman and Myszczak (2001) writing in mathematics class seems to demonstrate a student’s knowledge of material being taught and it allows for an outlet for true authentic assessment.

Much of the research indicates writing serves as a means of helping students organize, analyze, interpret, and communicate mathematical ideas, leading to a deeper understanding of content concepts (Burns, 2004, Holliday, Yore, and Alverman, 1994). Writing in the Math classroom can help students by allowing them to put together their thinking by requiring them reflect on their work and clarify their understanding of the ideas of the lesson. Many researchers suggest the use of journals in the Math classroom.

Writing can help student gain relevant knowledge and experience in preparing for new activities, review and consolidate what is known or has been learned, and reformulate and extend ideas and experiences (Langer and Applebee, 1987). In addition to Langer and Applebee, Kelly (2008) stated journals provide students the opportunity to 1) sort out experiences, solve problems and consider varying perspectives, 2) examine relationships with others and the world, 3) reflect on personal values, goals and ideals, and 4) to summarize ideas, experiences, and opinions before and after instruction.

Wilcox (2011) identified two levels of integration that teachers may use as a beginning point. Writing without revision, the first level, can be readily worked into mathematics instruction. Writing with vision, the second level, may take more time but enables teachers to connect the writing process more fully with mathematics instruction. Each level can be appropriate under differing circumstances. Regardless of which level of writing is used, the benefit to the student is a great tool in teaching students to become literate in Math.

To put the benefits of journal writing into perspective, Kostos and Shin (2010) conducted a study with a group of second graders to analyze how the use of journals affected their communication of Mathematical thinking. The results of the study found that the use of journals to enhanced second grade student’s mathematical thinking through math communication. Kostos and Shin findings showed improvement on student’s mathematical thinking through math communication, an increased use of Mathematics vocabulary and math journals worked as an assessment tool for student mathematical thinking.

One area in which is beneficial is that of problem solving. Writing increases understanding, achievement, problem solving skills (Bangert, Drowns, Murley, and Wilkinson, 2004, Borasi & Rose, 1989, Steele, 2005, 2007, Herrick, 2005, and Clark, Waywood and Stephens, 1993). It has been reported that low achieving students tend to be impulsive problem-solvers: they jump into a problem without understanding (Charles and Lester, 1984).

Huggins and Maiste (1999) stated children have an implied understanding of the word order of problems but their experience with verbal forms doesn’t connect their understanding. In other words, students understand the numerical form, but once in word form, most feel they lack skills to solve the problem. With journal writing the problem solving breakdown can be improved because students will have a better understanding of the word order and verbal forms because they are consistently using journal writing as a regular part of their Math instruction.

As the research has shown, journal writing has many benefits to students and teachers. Students can learn from their writings by processing information received from instruction and putting down on paper in their own words what they think they have learned from the lessons. In return, the teacher can review these journals and make assessments about what the student has learned and give additional instruction if patterns arise in the journals indicating that students do not understand the material. Importance of Vocabulary

We have seen how writing is important to literacy in Math, now we will look at the importance of vocabulary. According to Fletcher and Santoli (2003), vocabulary of math is not usually taught in school and if students are not reading good textbooks, then they have no place to read math terms. As mentioned earlier, Yang’s study on textbooks showed students needed assistance from outside sources to fully understand the complex texts. As teachers, we cannot always select the perfect textbook; we use what we’ve been given so it is us to the teacher to make the most out of the text.

Math vocabulary plays and important role in a student’s ability to understand daily lessons, complete homework, discuss ideas in groups, take tests and be successful in achievement tests (Amen, 2006). If vocabulary plays a primary role in so many aspects of math then it is important that vocabulary development be a part of Math instruction. Teachers need utilize strategies such as word walls, vocabulary journals, and other activities to stimulate the use of vocabulary in Math instruction.

Amen suggested the following strategies for achieving an understanding of math vocabulary: * Require use of mathematical language within the classroom * Create a glossary of terms that is available to all students and grows with each chapter * Use of word walls as a review of terms * Daily problem solving activities * Pre and post vocabulary inventories Amen also stated in her research that the direct instruction and support of math vocabulary increased test scores and confidence in test takers.

This is encouraging news when so much focus is placed on achievement test scores. The use of vocabulary activities in the classroom to help students more literate in math will also narrow the gaps in students who are lacking many of the basic skills, prior knowledge, and mathematical thinking stated earlier by Amen. Strategies for Teaching Literacy Writing and vocabulary are a very important part of Math literacy. For students to become literate, teachers need to include strategies in the classroom for students.

During the study conducted by Kester Phillips, Bardsley, Bach, & Gibbs-Brown (2000), as teams worked on lessons and making connections they began to realize that not only was their job to teach children mathematics and literacy skills and strategies, but it was also their job to help their students make connections between them and help them transfer these skills and strategies to other content areas. These strategies need to be a part of every lesson and used every day. Many students learn by repetition and the daily use of these strategies will drill these key pieces of information home.